ujjwalraj anitha@004140004 thick cylinder(1).docx

7/23/2019 ujjwalraj anitha@004140004 thick cylinder(1).docx

1/17

Laboratory reportThick Cylinder

Ujjwalraj Anitha (@00414004)Distribution, Transission systesand desi!ns"sc# $etroleu and !as en!ineerin!"odule co%ordinator& $ro'#Ali kadir


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ab e*ort on thick cylinder

Contents1. Objective......................................................................................................... 2

2. Abstract...........................................................................................................2

3. Introduction.....................................................................................................2

4. Theory............................................................................................................. 2

4.1 LAME Theory...............................................................................................2

!. Apparatus re"uired..........................................................................................!

#. $rocedure........................................................................................................ !

%. &esu'ts ( co)putation....................................................................................#

*. +iscussion.....................................................................................................1!

,. Conc'usion.....................................................................................................1!

&e-erences...........................................................................................................1#

List o- tab'es

Tab'e 1 +epth penetration /.#*............................................................................ #

Tab'e 2 +epth penetration 1.!*............................................................................ *

Tab'e 3 +epth penetration 2.2,..........................................................................1/

Tab'e 4 +epth penetration 3.#!..........................................................................12

Tab'e ! 0 error has been ca'cu'ated -or dierent penetrations..........................1!

List o- ure

iure 1 pressure in thic5 cy'inder........................................................................3

iure 2 Top vie6.................................................................................................. 3

List o- raph

7raph 1 8oop9 radia' stress :; 1;r2.....................................................................#

7raph 2 8oop and radia' strain :; 1;r2................................................................%

7raph 3 8oop and radia' stress :; r....................................................................*

7raph 4 8oop9 radia' stress :; 1;r2.....................................................................*

7raph ! 8oop and radia' strain :; 1;r2...............................................................,

7raph # 8oop and radia' stress :;s r..................................................................1/

7raph % 8oop9 radia' stress :; 1;r2...................................................................11

7raph * 8oop ( radia' strain :; 1; r2................................................................11

7raph , &adia' ( hoop stress :; r.....................................................................12

7raph 1/ 8oop9 radia' stress :; 1;r2.................................................................13

1


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7raph 11 8oop strain ( radia' strain :; 1;r2.....................................................14

7raph 12 8oop stress ( radia' stress :; r.........................................................14

1. ObjectiveTo e


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2@ Lonitudina' a


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+i!ure & To* -iew

ro) ure inner radius B &1and outer radius B&29

Cy'inder havin pressure p?interna'@ at distance r?radia'@9

The LAME= e"uation is iven by9

8oop stress 9

2

BA

r = +

Radial stressr

2r

BA

r =

Using boundary conditions,

Then the equations become,

4


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!. Apparatus re"uired

1@ A thic5 cy'inder 6ith outer dia)eter B 3/4)) ( inner dia)eterB

1!!)) attached 6ith ten strain aues at respective positions.

2@ 8ydrau'ic ra)

3@ Tapered p'u inside the bore

4@ 8ydrau'ic cy'inder to supp'y 'ubricatin oi'

!@ train aue

#@ +ata 'oer ?Solatron Schlumber3!3/@

#. $rocedure

To attain ero re-erence 'ubricatin oi' is pu)ped to the taperedp'u. The p'u is rotated at the sa)e ti)e durin the 'ubrication

to ensure uni-or)ity ti' the spira' roove is ''ed 6ith the oi'.

In case o- hydrau'ic ra)9 an initia' 6eiht 6as app'ied and

/.2#)) 6as obtained as initia' readin. o6 it is eroed and 1/

dierent channe's o- strain are initia'ised to the 'oin syste).

The operator pushed the hand pu)p do6n to -orce the hydrau'ic

ra) head ti'' the tapered p'u. i)u'taneous'y 'ubrication is done

6ith the he'p o- pu)p to ensure the uni-or)ity o- the ra) and

the oi' pu)p. ote do6n the readins o- strain.

!


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&eadins 6ere noted -or penetrations o- 4)) 6ith a step

dierence o- /.%!)). Lubrication is done si)u'taneous'y. Load

shou'd be re)oved 6hen you are ta5in the readins.

%. &esu'ts ( co)putation

a@ +epth o- penetration B /.#*

Table 1& De*th *enetration 0#./

#


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ra*h 1& oo*, radial stress 23 13r

From graph,

A= 5.4N/mm2

B= (0!"#$0#0!%&2 ' 0)= 57050N

*= !!+&mm2

By ame-s equation (theoretically%,

A=4.477.5

2

152277.5

2 = 1.545N/mm2

B=4.477.521522

15224.42 = 35711.18N

.n graph , r /& r and e , er /& &r2 are plotted

%


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ra*h & oo* and radial strain 23 13r

ra*h 5& oo* and radial stress 23 r

b@ +epth o- penetration B 1.!*

Table & De*th *enetration 1#6/

*


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From graph,

A= 9.9N/mm2

B= (1)$#%&2'0)= 184600N

*= 10 N/mm2

ame-s eqn,

A=1077.52

152277.52 = 3.51N/mm

2

B =1077.5

2152

2

15224.4

2 = 81161.79N

3i4en graph ,

r /& r ande ,

er /& &r2 5or penetration )6 has

been plotted

,


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ra*h 6& oo* and radial strain 23 13r

ra*h .& oo* and radial stress 23s r

c@ +epth o- penetration B 2.2,

1/


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Table 5& De*th *enetration #7


From graph,

A= 10.9N/mm2

B= (2012$")0%&2 ' 0)= 300600N

* = 20.2N(3raph%

By ame-s 5ormula,

A=20.277.5

2

152277.5

2 = 7.09N/mm2

B=20.277.5

2152

2

15224.4

2 = 163946.81N

.n graph ,

r /& r ande ,

er /& &r2 ( penetration 22% has been

dra7n belo7

11


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ra*h /& oo* 9 radial strain 23 13 r

ra*h 7& adial 9 hoo* stress 23 r

d@ +epth o- penetration B 3.#!

Table 4& De*th *enetration 5#.6

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From graph,

A= 22N/mm2

B= (!1$!!62%&2'0)= 472150N

*=30N

By ame-s theory,

A=3077.5

2

152277.5

2 = 10.53N/mm2

B=3077.5

2152

2

15224.4

2 = 243485.37N

3raph o5

,

r /& r ande

,

e

r /& &r2 ( penetration "1)% has been

dra7n belo7

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ra*h 11& oo* strain 9 radial strain 23 13r

ra*h 1& oo* stress 9 radial stress 23 r

$ercentae error ca'cu'ations

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Table 6& : error has been calculated 'or di;erent *enetrations

*. +iscussion >hen the p'u penetration increases9 the pressure inside the

cy'inder a'so increases. >hen the depth o- penetration is /.#*))9

the interna' pressure beco)es 4.4;))29 and by increasin the

deepness to 1.!*9 2.2,9 ( 3.#!))9 the re'ated pressure va'ues are

1/9 2/.2 ( 3/;))2 respective'y. The -o''o6in strain readins -or

dierent heihts 6ou'd va'idate the increase in va'ues o- interna'

pressure.

Fy co)parin the va'ues o- theoretica' ( e


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&e-erences

Fhavi5atti9 . . Mechanics Of Solids. e6 +e'hi e6 Ae

Internationa' Ltd.9 2/1/. $rint.

8earn9 E. ?1,,%@. Mechanics of materials. O

ujjwalraj anitha@004140004 thick cylinder(1).docx

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